Computationally driven high-throughput identification of CaTe and ${\mathrm{Li}}_3\mathrm{Sb}$ as promising candidates for high-mobility $p$-type transparent conducting materials

High-performance $p$-type transparent conducting materials (TCMs) must exhibit a rare combination of properties including high mobility, transparency, and $p$-type dopability. The development of high-mobility/conductivity $p$-type TCMs is necessary for many applications such as solar cells or transparent electronic devices. Oxides have been traditionally considered as the most promising chemical space to dig out novel $p$-type TCMs. However, nonoxides might perform better than traditional $p$-type TCMs (oxides) in terms of mobility. We report on a high-throughput computational search for nonoxide $p$-type TCMs from a large data set of more than 30 000 compounds which identified CaTe and ${\mathrm{Li}}_3\mathrm{Sb}$ as very good candidates for high-mobility $p$-type TCMs. From our calculations, both compounds are expected to be $p$-type dopable: intrinsically for ${\mathrm{Li}}_3\mathrm{Sb}$ while CaTe would require extrinsic doping. Using electron-phonon computations, we estimate hole mobilities at room temperature to be about 20 and $70{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ for CaTe and ${\mathrm{Li}}_3\mathrm{Sb}$, respectively. These are “upper bound” values as only scattering with phonons is taken into account. The computed hole mobility for ${\mathrm{Li}}_3\mathrm{Sb}$ is quite exceptional and comparable with the electron mobility in the best $n$-type TCMs.

Figure 1

From the left to the right, the conventional cells, band structures, projected density of states (DOS), and relaxation time and scattering rate. Panels (a)–(d) and (e)–(h) show data of CaTe and ${\mathrm{Li}}_3\mathrm{Sb}$, respectively. The conventional cells present local environments around cations Ca (blue) and Li (green). Panels (b) and (f) plot DFT band structures with a rigid shift of the conduction bands (scissor operator) to fit the fundamental gaps computed by $G_0{W}_0$. Panels (d) and (h) show relaxation time $\tau$ (in femtoseconds) and scattering rate $1/\tau$ (in 1/second) as functions of energy at temperature 300 K. The projected DOS in (c) and (g) are computed by DFT. The band gaps of the DOS and relaxation time are also shifted to fit $G_0{W}_0$ values.

Figure 2

The indirect optical absorption of ${\mathrm{Li}}_3\mathrm{Sb}$ due to phonon-assisted transitions.

Figure 3

Phonon band structures with fat bands representing displacements of atomic vibrations. The width of fat bands gives qualitative understanding of the vibrational modes such as what are the atomic types involved in the vibrations at a given energy, their direction of oscillation, and the amplitude (related to the displacement). The projected DOS of phonons on each type of atom are correspondingly shown next to the band structures. (a) CaTe and (b) ${\mathrm{Li}}_3\mathrm{Sb}$.

Figure 4

Hole mobilities as a function of hole concentrations of CaTe and ${\mathrm{Li}}_3\mathrm{Sb}$ at temperatures 300 and 400 K.

Figure 5

The defect formation energy as a function of Fermi level of intrinsic and extrinsic defects for (a) $\mathrm{CaTe}$ and (b) ${\mathrm{Li}}_3\mathrm{Sb}$. For $\mathrm{CaTe}$, the intrinsic defects include vacancies (${\mathrm{Vac}}_{\text{Ca}}$ and ${\mathrm{Vac}}_{\text{Te}}$), antisites (${\mathrm{Te}}_{\text{Ca}}$ and ${\mathrm{Ca}}_{\text{Te}}$), and interstitial atoms inserted into the tetrahedral hollows formed by 4 Te atoms (${\mathrm{Ca}}_{\text{i(tet,Te4)}}$ and ${\mathrm{Te}}_{\text{i(tet,Te4)}}$), while Na, K, and Li are used as the extrinsic defects substituting Ca atoms (${\mathrm{Na}}_{\text{Ca}}$, ${\mathrm{K}}_{\text{Ca}}$, and ${\mathrm{Li}}_{\text{Ca}}$). For ${\mathrm{Li}}_3\mathrm{Sb}$, the intrinsic defects include vacancies (${\mathrm{Vac}}_{\text{Li-1}}$, ${\mathrm{Vac}}_{\text{Li-2}}$, and ${\mathrm{Vac}}_{\text{Sb}}$), antisites (${\mathrm{Li}}_{\text{Sb}}$, ${\mathrm{Sb}}_{\text{Li-1}}$, and ${\mathrm{Sb}}_{\text{Li-2}}$), and interstitial atoms inserted into the octahedral hollows formed by Sb and Li atoms (${\mathrm{Li}}_{\text{i(oct,}}\text{Sb2Li4)}$, ${\mathrm{Li}}_{\text{i(oct,}}\text{SbLi5)}$, ${\mathrm{Sb}}_{\text{i(oct,}}\text{Sb2Li4)}$, and ${\mathrm{Sb}}_{\text{i(oct,}}\text{SbLi5)}$). In both cases, the VBM is set to zero.